Inference

Inference is the act or process of reaching a conclusion about something from known facts or evidence.

For example, based on perceiving that the ground is wet, one can infer that it likely rained that day.

Logical Inferences #

Logical inferences relate two or more mental representations with structure and reasoning.

Disjunctive Syllogism #

If $A \lor B$, and $\lnot A$, then $B$ must necessarily be true. (This is the same rule formalized in propositional-logic.)

Call’s cup task: Suppose a researcher puts a prize in one of two cups, and shows that one of them is empty. Using logical reasoning, we can deduce that the prize must be in the other cup.

• This has been studied in other animals using both visual and auditory inference. For instance, if the researcher shakes a cup and it makes no sound, chimpanzees can deduce that the prize must be in the other cup.
• One confounding factor is that this behavior can be explained by simple exploration: if animals are able to recognize that the empty cup has already been explored, they will simply try all other options. (‘avoid empty’ heuristic)
  • can be ruled out by having one option in each cup, and revealing one of the cups. Chimps will still choose the other cup even though both were full
• maybe A maybe B interpretation: the two mental representations of the prize being in cup A vs cup B are not related, but when one cup is presented as empty one of them is deleted so the only representation remaining is chosen out of necessity.
  • can be ruled out by running two cup tasks simultaneously (one in A or B, one in C or D). When cup A is revealed, individuals with logical reasoning will choose cup B since it has a 100% chance of having a prize, whereas C and D have a 50% chance.
    • 4 cup test success rate increases over age in human children: logical inference begins to appear at around age 3-5.
      • Why? the concept of “A or B” logic is learned through linguistic interaction. When parents say “or”, children learn what it means and apply it to logical reasoning
    • Chimps do not succeed in the 4 cup test, which suggests they use the ‘maybe A maybe B heuristic’. But absence of evidence is not evidence of absence, so this doesn’t rule out completely that chimps have logical reasoning. It’s possible that the 4 cup task requires too much working memory for them.

Categorical Syllogism #

If $A \subset B$ and $B \subset C$, then $A \subset C$.

There is currently no cross-cultural data on the development of logical reasoning. This is still a rapidly evolving field, and we are not sure the extent to which logical reasoning exists in innate knowledge, or is learned through social interaction.

Perceptual Inference #

Our ability of perceptual inference demonstrates that inference is not something we necessarily have to do consciously: our brain can automatically and near-instantly make assumptions about the world that change our perception of it.

Statistical Inference #

Piaget’s theory: statistical inference develops relatively late in development. Newer findings: statistical inference develops before verbal communication. (Xu, Garcia 2008)

• mean looking time increased when samples were unexpected given population

A researcher has two populations, one of mostly red balls and one of mostly blue balls. If they draw a sample from one without telling a participant which, they should be able to determine which population it was most likely drawn from using statistical inference.

• ability to distinguish between population and sample
• Rakoczy et al 2014: chimpanzees have statistical inference abilities and will choose to sample from a population with the highest proportion of treats.

Statistical inference is an example of inductive inference: the ability to generalize outcomes to explain other aspects of reality. (example: generalize sample to population) For the formal statistical framework, see hypothesis testing and parameter estimation.

Kushnir, Xu, Wellman 2010: children can infer that the less prevalent something is in a population, the stronger the preference for that thing if it is chosen consistently

Causal Inference #

Understanding of the cause-effect relation

• may be confounded with associative learning: main difference is causal inference applies when seeing something for the first time

diagnostic reasoning: ability to analyze a causal chain backwards: upon observing an effect, infer what caused it

Gopnik & Sobel 2000: children 2-3 years of age reliably demonstrate causal inference with associating colors with actions Walker & Gopnik 2014: toddlers 18-30 months of age can infer higher-order relational principles in causal learning

Although there is little cross-cultural data, some preliminary research suggests that causal inference ability is independent of culture